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Center for Nonlinear Studies |
As a consequence of carefully designed lattice geometries, two-dimensional mechanical metamaterials can exhibit a variety of material response and functionality not found in ordinary materials. For many two-dimensional metamaterials, the architecture may be approximated as a set of discrete, spin-like internal degrees of freedom, and the overall metamaterial response may be tuned by designing the interactions and geometry of these “spins.†Such a spin picture is useful for finding interesting compatible architectures in which all internal displacements match, and hence which gives the material a global, zero energy floppy mode. Inverting this usual approach, we set out to investigate the consequences of incorporating instead of avoiding frustration into a two-dimensional mechanical metamaterial. Such frustration results in “prestress,†internal stresses in the reference state of the material that cannot be eliminated but that may be rearranged and manipulated in multiple ways. Inspired by a frustrated geometry taken from the field of “Arificial Spin Ice,†we introduce a material design that has many surprising properties: As has been seen several previous studies on such frustrated designs, triangular arrays of bistable beams and square arrays of bistable domes, the continuous nature of mechanical degrees of freedom creates pathways for the inherent frustration to be partially relieved, which usually cannot occur in magnetic systems. There is a global, ordered, unique ground state arrangement of the internal prestress. However, since the mechanical lattice inherits the frustrated geometry of the underlying spin ice, a manifold of higher energy, disordered, yet stable configurations can still be accessed. Through simulations and 3d-printed experimental prototypes, we also demonstrate a novel path dependence of the internal configuration that arises due to the bistability of a subset of the internal degrees of freedom. I will outline the mapping from the spin ice to the metamaterials, the consequences of the frustrated lattice geometry, simulation predictions for the novel disordered, multistable stress distributions, and current progress on 3d-printed experiments.
Host: Cristiano Nisoli